I just did the first one using Newton's Method and got what I was looking for. The second problem I posted seems to be a little tougher and I need help with that one.

Edit: My only problem with the first one is I don't know what to use an initial approximation. It took me almost two pages to get the answer. Can anyone tell me a faster way to get an approximate number eight decimal places?

Edit: My only problem with the first one is I don't know what to use an initial approximation. It took me almost two pages to get the answer. Can anyone tell me a faster way to get an approximate number eight decimal places?

get a computer to do the calculating for you. I can't imagine why anyone would be learning Newton's method without some mathematical programming environment, eg. Haskell interpreter, R gui.

I just did the first one using Newton's Method and got what I was looking for. The second problem I posted seems to be a little tougher and I need help with that one.

Edit: My only problem with the first one is I don't know what to use an initial approximation. It took me almost two pages to get the answer. Can anyone tell me a faster way to get an approximate number eight decimal places?

Hello,

I would draw a rough sketch of the 2 graphs. For instance with #1:
Draw the graph anf . Use the estimated x-value of the intersection as an initial value.
When I used I got the result with 8 decimals exact after 3 steps.

to #2. If n is a large number then . If you use a value a little bit larger than 1 as an initial value it will be sufficient. But with your example the sequence of x-value converges very slowly. So when I used it took me more than 20 cycles to get a nearly exact value.

I would draw a rough sketch of the 2 graphs. For instance with #1:
Draw the graph anf . Use the estimated x-value of the intersection as an initial value.
When I used I got the result with 8 decimals exact after 3 steps.

to #2. If n is a large number then . If you use a value a little bit larger than 1 as an initial value it will be sufficient. But with your example the sequence of x-value converges very slowly. So when I used it took me more than 20 cycles to get a nearly exact value.

Thanks for helping me. Yeah for it took me around 20 cycles. I'm going to probably get a number closer to one so I can fit it on half a page. Thanks for your assistance.